Wave transmission network



May 27, 1947.

w. P. MAscJN WAVE TRANSMISSION NETWORK Filed May l5, 1945 MAM. Rw .Lummomm \b U \N J .,IH FH" `N g Qu ma En @Nw am, m6 wm 5 on n ,mi

. W @Dx /NVENroR W P. MASON A TTORNE V Patented May 27, 1947 ZAZLBS 2,421,033 WAVE TRANSMISSION NETWORK Warren P. Mason, West Orange, N. J., assigner to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application May'15, 1943, Serial N0. 487,081

1G Claims. 1

This invention relates to wave transmission networks and more particularly to branching circuits comprising two parallel-connected wave filters made up of sections of transmission line for combining or separating two different bands of frequencies.

The principal object of the invention is to place upon a common transmission line simultaneously two bands of frequencies from different sources or to separate into individual channelsvtwo bands simultaneouslytransmitted by one line.

Other objects are to broaden the transmission bands, sharpen the cut-offs and increase the transmission efficiency of the individual channels and increase the discrimination between channels.

. When a transmission line is to be supplied with two bands of frequencies from different sources or when signals on a line are to be separated into individual channels on a Yfrequency basis a branching circuit is required. Often it is desired that the channels be capable of transmitting efficiently comparatively Wide bands, with sharp cut-offs. High discrimination between channels is also often desirable. Always there is the requirement that the presence of one channel does not decrease unduly the transmission efficiency-of the other channel; Simplicity in mechanical structure is also of importance in cost reduction. Y l 1 f The present invention provides a branching circuit which fulfills the above requirements in a compact, fully shielded structure especially adapted for use in thevhigher frequency ranges f the order of hundreds of megacycles. The circuit comprises two wave filters connected to the common transmission line in parallel. The filters are of the ladder type, are shunt terminated and each comprises one or more sections. The filters may be designed to transmit substantially any desired Width of band. The discrimination between channels may be increased to any required amount by adding sections. The image impedances of the filters are chosen to match the impedance of the terminal loads with which they are associated. The component impedance elements used in the filters are sections of 'transmission line. Such elements have low vdissipation and therefore provide high transmission efciency within the band and sharp cut-offs. If coaxial line is used for the sections the outer conductors may be grounded, thereby providing almost perfect shielding for the structure. f n

In order that the two filters may operate in pereueI without adversely effecting the transmis- 5 5` Fig.

- the band of theother lter.

alleled end, each filter have a high input impedance over the band of the other. Special arrangements are provided to accomplish this. The terminating shunt branch at the paralleled end of the higher frequency filter is a section of transmission line short-circuited at its distant end. The filter also has at this end a building-out section of line the length and characteristic impedance of which are chosen to provide at the junction of the filters a high shuntingA impedance over One way of ac complishing this is to make 'the building-out section and the shunt branch of the same characteristic impedance and with'a combined length approximately equalto an odd multiple of a quarter wavelength" at'themid-band frequency of the other! filter.f 'Theterininating shunt branch at the paralleled, end -of the. lower frequency filter is made up of two tandem-,connected sections of line havingdiferent characteristic impedances proportioned'` vto provide an antiresonanceV at kthe midebandrequency .of that filter and a resonanceeatlthe mide-band frequency of the other' lter'. For ease of computation the two sectionsV may beniade 'of the` same length and the second section `may be short-fcircuited at its distant end. An vimpedance-irvert'ing section of line, having a lengthapproximately .equalto an oddmultiple of'. a quarter wavelength at'lthe Vmid-band frequency lof the higher Vfrequency filter, is added atfthel'paralleled end of the' lower frequency filtert'oprovide at the junction of the filters a high' shunting impedanceover the band'of the higher frequency filter. v y s.

If. either theband widths or. the mid-band frequencies of theet'wo channels may be chosen at will thev outer conductors of allof the component coaxial elements usedin the filters may be Vmade offtheisame diameter,A `thus considerably simplifying the mechanical structure and reducing the cost...

The natureotthe invention will be more fully,`

Fia'liandg y .v 1 i, Y Y 4 gives the impedance-frequency charac- 3 teristic of the shunt branches of the lower frequency lter.

In Fig. l a common transmission line I branches into two channels 2 and 3. All of these lines may, for example, be of the coaxial type, comprising a hollow cylindrical outer conductor 4 and concentric therewith an inner conductor 5 which may be either solid or hollow. The channels 2 and 3 may be supplied from separate sources with bands of'signals having mid-band frequencies of fm1 and fm2, respectively, which are combined in the common line I, or the line I may carry the two bands which are to be separated into the individual channels 2 and3, as indicated by the double-pointed arrows. u Thewcornbinin'g" or separating is accomplished by means of the two band-pass wave lters 8 and 9 which are connected in parallel to the line I atthe junction point I9.

The lters 8 and 9 are of the ladder type, comprising shunt impedance branches and interposed series impedance branches, and are shunt-terminated at each end. The lter 8, shown as a single-section structure, comprises two identical shunt branches VI2 and I3', an interposed series branch I4 and an impedanceginverting section of line I5 connected between tthe shunt branch I3 andy the junction point I0. The lter 9, also shown asA a' single-section structure, comprises two identical shunt branches II and I8, an interposed series branch I 9 and a building-out section of line 28 connected between the branch II and the junction III. TheV discrimination between the' channels 2 and 3 may, of course, be increased to any required extent simply by adding more sections to the lters 8 and 9. All of the component impedance branches of the lters are formed by sections of transmission line. As shown, these are of the coaxial type. The branch I'I, for example, has a' cylindrical outer conductor 22 and concentric therewith an inner conductor 23, Each of the shunt branches I2 and I3 ofthe filter 8 is constituted by two sections of line 24 and 25, having inner conductors 26Y and 2T, connectedin tandem., Each of the shunt branches I2, I3, I'I ,and I8 is short-,circuited at its distant end as, forexample, bythe conductive end plate 28 on the branch I8. The use of coaxial lineA sections has the advantage that the outerconductors may all be grounded, or otherwise fixed in potential,A as shown at 29, thus providing substantially perfect shielding for the entire structure. Other types of line sections may, however, be used in some circumstances. In Fig. 1 portions of the line sections I4 and 28 have been removed in order to save space.

The electrical design of the lters will now be considered. It will be assumed that the filter 8 is required to transmit a band of frequencies eX- tending from ,fu to' f2; with a mid-band frequency of fm1., which isV the geometric mean of the two, and the lter 9 a higher band between ,112 and fzzlwith a mid-band frequency fm2. The design may beworked out most conveniently by referring to the equivalent, electrical circuit which, for the filter v9, isshown in Fig'. 2. The circuit is an unbalanced, singlelsection, three-element, ladder-type structurewith yinput terminals 30, 3| and output terminals 32, 33. The shunt branches at the ends of the lter, each 'comprising a capacitance C22 and an inductance L22 connected in parallel, are furnished by the line sections I'I and I 8 which are identical. The series inductance Li and the two shunt cap'acitances` C12 at the ends thereof represent theline section I9.

The approximate values of these elements in terms of the lengths and characteristic impedances of the line sections are given by the following formulas:

in which A and B are the lengths in centimeters of the line sections I9 and I8, respectively, Zoi and Zo2 are, respectively, the characteristic impedances and V is the velocity of propagation in the sections, which may be taken as 3 X l010 centimeters per second. It is assumed that the distributed resistance and conductance of the line' sections are smal-l enough to be neglected. In Equation 4 the factor 8/1r2 is used because the section I8 is in the neighborhood of a quarter Wavelength long and is short-circuited at the end. In this connection reference is made t Equation 2.139 and the accompanying discussion on page 65 of applicants book Electromechanical Transducers and Wave Filters pub-v lished by D. Van Nostrand, Inc.-

The circuit'y of Fig. 2 will be recognized as the filter designa-ted Type IIIeV on page 316 of Transmission Networks and Wave Filters by Shea, also published by D.- Van Nostrand, Inc. The follow# ing design formulas may be used:

21" (f22'-fi2)ZK where ZK is the image impedance of the ltei at the mid-band frequency fm2. In comparing Equations 6 and 7 with the corresponding ones given by Shea it should be remembered, that applcants lter has a mid-shunt termination.,

A suggested design procedure for the lter 9 will now be outlined. It will be assumed that the common line I and the channels 2 and 3 .all have the same characteristic impedance ZoK. The image impedancemZ'K of the filter is, therefore, chosen equal to 4Zon toV provide an impedance match at the junctions of the lter and the lines. 'I'he cut-off frequencies h2 and f2s arel chosen and the required valuesof the elements L12, L23 and the sum of C12 and C22 are computed from Equations 5, 6 and '7 The value of L22 found from Equation 6 is now substituted in lEquation 4 and the required length'B of each of the shunt sections I'I and I8 is found assuming, for a reason to be explained below, that thecharacteristic impedance Zo2 is equal to ,Zone Next, the value of C22 is found from Equation 2. vSince the sum of C12 and C22 is known from Equation 7 the value of C12 may now be found.V This value of Ca2 is substi tutedI in Equation 1, thevalue of L12 found from Equation 5 is substituted in Equation 3 and the two equations rsolved simultaneously for the required lengthA and characteristic impedance Zai of the series branch I9,

At the junction point I0 the ilter 9 must have a high input impedance at the4 mid=band frequency fm1 of the lower frequency filter 8. At this frequencyl the input impedance will be approximately the impedancecfY the shunt branch I1, which is a section of line short-circuited at its distant end. In order to build this up to a high valuea building-out section of transmission line 20 of characteristic impedance ZuK is connected betweenthe junction point I6 and the shunt branch I'I. .Since the branch Il also has a characteristic impedance of ZoK, it is only necessary to make the. length D of the section 20 plus the length B of the branch Il approximately equal to an odd multiple of a quarter wavelength at the frequency fm1. That is,

wheren is any integer'but is usually taken as unity. The characteristic impedance Zoz of the shunt branch Il might have been chosen as something diferent frornZoK but in that case the sim- -ple relationship given by Equation 8 for the length D of the building-out section 20 would not hold.

It is seen that the line sections I1, I8 and 2E) all have the same characteristic impedance, namely, ZvK. It is possible, by proper choice of the cut-off frequencies frz and Jzz, to make the characteristic impedance Zul of the series section I 9 also equal to Zon. If this is done, then the entire filter 9 may be constructed out of a single size of coaxial line, thus simplifying the assembly and reducing the cost.

The design of the lower frequency filter 8 will now be considered in more detail. To prevent the lter 8 from adversely affecting the operation of the lter 9, it is necessary that the input impedance of the former at the point of junction Ill be high over the transmission band of the latter. The length E of the impedanceinverting section I is, therefore, made approximately equal to an odd multiple of a quarter wavelength at the mid-band frequency fm2 of the filter 9, that 1s,

where n is any integer but is usually taken as unity. Thev input impedance Z of the shunt branch I3 must be lowl over the band of the filter 9. This may be accomplished by making the branch I3 resonant at fm2. It is also required that Z be high over the transmission band of the lter 8. This is clone by making the branch I3 antiresonant at fm1. In order to get a wide spacing between the resonance and antiresonance used, thevshunt branch I3 is preferably made up of two sections of transmission line 24, 25 having different characteristic impedances ZoA and ZoB, respectively, with the second section 25 shortcircuited at its distant end. If the distributed resistance and conductance are neglected and the sections 24 and 25 have the same length F, the impedance Z is given by the expression where w is equal to 21r times the frequency f. If the impedance ZoA is smaller than the impedance ZOB the impedance Z plotted against frequency will be of the form shown in Fig. 4. The resonances occur when the numerator in Equation 10 is'zero, that is, when the total length 2F of the section I3 is a multiple of a half wavelength. Inequation form where n is any integer. The first three resonances fm, fRz and fas are shown in Fig. 4. The antiresonances occur where the denominator in Equation l0 is zero, that is, when The first three antiresonances fm, faz and .fsa are shown. If Zo. and Zon were equal the antiresonance would occur at equal frequency intervals. However, by making ZoA smaller than vZon the odd antiresonances Ai and :fsa are lowered in frequency and the even antiresonances, such as JAz, are raised. The result is that in the neighborhood of the odd resonances fin and fRa there is a considerable frequency space between resonance and antiresonance.

The length 2F of the shunt branch I3 is therefore so chosen that one of the odd resonances fm, fas or a higher one occurs at the mid-band frequency fm2 of the higher frequency filter 9. If the frequency spacing between the two mid-band frequencies fm1 and fm2 is not too great, the rst resonance fm may be used. However, when this spacing is considerable it is preferable to use fRa or a higher resonance. If fea is used the length 2F will be 3/2 wavelengths at fm2 and the length F may be found from Equation 11 by taking n as three and w as 21; fm2, that is,

The first antiresonance JAi will now be placed at the mid-band frequency of the lower frequency lter 8. As explained above, the antiresonances depend upon the ratio of the characteristic impedances ZoA and Zon of the two lengths of line 24 and 25. The required ratio may be found from Equation 12 by taking F as the length found from Equation 13 andsetting w equal to 297 fm1, that S,

The next step is to determine the characteristic impedances ZoA and ZOB of the sections 24 and 25 and the diameters of the conductors. Here certain mechanical and electrical considerations must be kept in mind. The outer conductors may conveniently have the same inner diameter b as that used in the sections ofthe filter 9. The diameter a of the inner conductor of a coaxial line is related to the diameter b and the characteristic impedance Zo by the formula Y Zo 60105-2l so'that the inner conductor 2B and outer conductor of the lower impedance section 24 will have sulhcient separation to prevent a Voltage breakdown, After the impedance Zes has been chosen, the impedance ZoAis found from Equation 14 andthe diameters a1 and a2 of the inner conductors 26 and 21 from Equation 15. In order toY avoid the formationl of acorona discharge in the branch I3, the end of the inner conductor 26, where it joins the inner conductor 2'I, should be rounded off as shown at 34. Each length F will then be measured from the point where the diameter of the inner conductor is the average of a1 and a2. The shunt branch I2 will be identical with the branch I3.

There remains now only to determine the series branch i4 of the filter 8. The equivalent electrical circuit of the filter, which is similar to that of the lter 9, is shown in Fig. 3. The series inductance L11 and the two shunt capacitances C11 at the ends thereof, representing the line section i 4, have' the values G O11 W0; (l5) where G is the length of the section I4 and Z112 is its characteristic impedance. The shunt branches at the ends of the lter, each comprising a capacitance C21 and an inductance L21 connected in parallel, represent the shunt branches I2 and I3 in the neighborhood of the mid-band frequency fm1 which coincides with the rst antiresonance at fin, By analogy with the procedure followed on pages 63 to 65 of applicants above-mentioned book, C21 and L21 may be evaluated as L21 hCIlllSS The -lter design formulas, which are similar to Equations 5,16 and 7 above", are

Since the length F and the impedance Z011 have been determined, the value of C21 may now be found from- Equation 18. Since the mid-band frequency fm1 has also been selected, the value of L21 may be found from Equation 19. This value of L21 is now substituted in Equation 21 and the' cut-off frequencies- ,T11 and fai so chosen that Equation 21 is satisfied, keeping in mind that fml=m These values of fn and fn arev substituted in Equation 2D to find L11 and' in Equation. 22 to find the sum of C11 and' C21. Since the value of C21 hasV already been determined, the value of C11. may be found. These values of C11 and L11 are` now substituted in Equations' 16 and 17, r'espectively, and the equations solved simultaneously for the length G of the section te and its characteristic impedance" Z112. There remains new only to hd the diameters of the conductors 8 forV the, section I4. The outer conductor may conveniently be made of the same diameter as the outer conductors used in the other component line sections of the filters. The diameter of the inner conductor may be found from Equation 15.

The above formulas for the lengths of the coaxial sections are based on the assumption that the concentric outer conductor will extend for the full. length of the section. As is apparent in Fig, 1, however, when a side branch is connected at the end of a series branch at least a portion of the outer wall will be missing at the connected ends of the sections. To correct for this condition the lengths of the line sections must be increased somewhat. This factor is of more importance in the higher frequency lters. In the case of the shunt branches it has been found that a more nearly correct result will be obtained if the length is measured from the outer conductor of .the series branch as shown, for example, by the dimension B for the branch I8.

What is' claimed is:

1. In combination, two Wave filters connected at one end, one of said lte'rs comprising a series impedance branch and a shunt impedance branch, said series branch being connected be'- tvv'een said shunt branch and the junction 0f said filters and being constituted by a section of transmission line having a length approximately equal to an integral number of quarter wavelengths at the mid-band frequency of the other of said filters and said shunt branch comprising two tandem-connected sections of transmission line having different characteristic impedances and. having their lengths and characteristic impedances chosen to make said branch antiresonant' near the mid-band frequency of said one lter and resonant near said mid-band frequency of said other filter.

2. The combination in accordance with claim 1 in which said mid-band frequencies are widely spaced in frequency and said shunt branch has at least two intermediate resonances occurring in the frequency range between said mid-band frequencies.

3. The combination in accordance with claim 1 in which said mid-band frequency of said` one lter is located near the rst antiresonance of said shunt branch and said mid-band frequency of said other filter is located near the third resonance of said shunt branch.

4.V The combination in accordance with claimV 1 in which said shunt branch is short-circuited at its distant end.

5. Thev combination in accordance with claim l inwhi'c'h said sections of line in said shuntbranch have approximatelyV the same length.

6. The combination in accordance with claim 1 in which said` sections of line in said shunt branch are' of the coaxial type` having outer conductors ofthe same inner diameter.

7. The combination in accordance with claim l in which said sections of line in said shunt branch are of the' coaxial type `having outer conductors of the same inner diameter and inner conductors which differ from each other in diameter, said inner conductor of larger diameter being associated with said tander11-connected section of lin'e nearer! to said series branch.

s.. In combination, two wave filters and an impedance-inverting" section of transmission line, said lters being connected in parallel at one end, one ofsaid filterscom'pri-si'ng ashunt branch, said impedance-inverting section being connected between said shunt branch and the junction of said lters and having a length approximately equal to an odd multiple of a quarter wavelength at the mid-band frequency of the other of said filters and said shunt branch comprising two tandemconnected sections of transmission line having diierent characteristic impedances and having their lengths and characteristic impedances chosen to make said branch antiresonant near the mid-band frequency of said one lter and resonant near the mid-band frequency of said other lter.

9. The combination in accordance with claim 8 in which all of said sections of line are of the coaxial type having outer conductors of the same inner diameter.

10. The combination in accordance with claim 8 in which said one filter includes a series impedance branch constituted by a section of transmission line the length and characteristic impedance of which are so chosen that both of said filters have the same image impedance at the mid-band frequency.

11. 'I'he combination in accordance with claim 8 in which said one filter has a lower mid-band frequency than said other lter.

12. The combination in accordance with claim 8 which includes a building-out section of transmission line, said other lter comprising a shunt branch constituted by a section of transmission line short-circuited at its distant end, said building-out section being connected between said shunt branch of said other filter and said junction of said lters and the combined lengths of said building-out section and said section of line in said shunt branch of said other filter being approximately equal to an odd number of quarter 10 wavelengths at the mid-band frequency of said one filter.

13. In combination, two wave lters and a building-out section of transmission line, said filters being connected in parallel at one end, one of said filters comprising a shunt branch constituted by a section of transmission line shortcircuited at its distant end, said building-out section being connected between said shunt branch and the junction of said filters and the combined lengths of said building-out section and said section of line in said shunt branch being approximately equal to an odd number of quarter wavelengths at the mid-band frequency of the other of said lters.

14. The combination in accordance with claim 13 in which said one iilter has a higher mid-band frequency than said other lter.

15. The combination in accordance with claim 13 in which both of said sections of line have the .same characteristic impedance.

16. The combination in accordance with claim 13 in which said sections of line are of the coaxial type having outer conductors of the same inner diameter and inner conductors of the same diameter.

WARREN P. MASON.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 2,064,775 Wheeler Dec. 15, 1936 2,196,272 Peterson Apr. 9, 1940 2,201,326 Trevor May 21, 1940 

